Exact numerical calculation of the density of states of the fluctuating gap model

Bartosch, Lorenz; Kopietz, Peter

doi:10.1103/physrevb.60.15488

Cited by 31 publications

(66 citation statements)

References 15 publications

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“…Its DOS and localization length have a long history of analysis [8,28,29,30]. The spectrum of U , together with the asymptotic behavior of the corresponding eigenstates Ψ z , which as we shall see is determined by b z , have the same information content as the input signal u(t).…”

Section: Introductionmentioning

confidence: 92%

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

Kazakopoulos

Moustakas

2008

Phys. Rev. E

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We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive non-linear Schrödinger equation with a Gaussian random pulse as initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of scattering data of the Zakharov-Shabat operator that determine the asymptotics of the eigenfunctions. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of information transmission through non-linear optical fibers.

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Section: Introductionmentioning

confidence: 92%

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

Kazakopoulos

Moustakas

2008

Phys. Rev. E

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“…However, Tchernyshyov has pointed out the technical error of the Sadovskii's solution, which is actually an approximation [ 388]. A sophisticated numerical method has shown that the Sadovskii's solution is qualitatively a good approximation for the complex order parameter [ 389,390]; the commensurate CDW is not the case, but the SC is the case. Then, the accuracy of the approximations usable in higher dimensions has been investigated [ 389].…”

Section: Mf Cmentioning

confidence: 99%

Theory of superconductivity in strongly correlated electron systems

et al. 2003

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In this article we review essential natures of superconductivity in strongly correlated electron systems (SCES) from a universal point of view. First we summarize experimental results on SCES by focusing on typical materials such as cuprates, BEDT-TTF organic superconductors, and ruthenate Sr 2 RuO 4 . Experimental results on other important SCES, heavy-fermion systems, will be reviewed separately. The formalism to discuss superconducting properties of SCES is shown based on the Dyson-Gor'kov equations. Here two typical methods to evaluate the vertex function are introduced: One is the perturbation calculation up to the third-order terms with respect to electron correlation. Another is the fluctuationexchange (FLEX) method based on the Baym-Kadanoff conserving approximation. The results obtained by the FLEX method are in good agreement with those obtained by the perturbation calculation. In fact, a reasonable value of T c for spin-singlet d-wave superconductivity is successfully reproduced by using both methods for SCES such as cuprates and BEDT-TTF organic superconductors. As for Sr 2 RuO 4 exhibiting spin-triplet superconductivity, it is quite difficult to describe the superconducting transition by using the FLEX calculation. However, the superconductivity can be naturally explained by the perturbation calculation, since the third-order terms in the anomalous self-energy play the essential role to realize the triplet superconductivity. Another important purpose of this article is to review anomalous electronic properties of SCES near the Mott transition, since the nature of the normal state in SCES has been one of main issues to be discussed. Especially, we focus on pseudogap phenomena observed in under-doped cuprates and organic superconductors. A variety of scenarios to explain the pseudogap phenomena based on the superconducting and/or spin fluctuations are critically reviewed and examined in comparison with experimental results. According to the recent theory, superconducting fluctuations, inherent in the quasi-two-dimensional and strong-coupling superconductors, are the origin of the pseudogap formation. In these compounds, superconducting fluctuations induce a kind of resonance between the Fermi-liquid quasi-particle and the Cooper-pairing states. This resonance gives rise to a large damping effect of quasi-particles and reduces the spectral weight near the Fermi energy. We discuss the magnetic and transport properties as well as the single-particle spectra in the pseudogap state by the microscopic theory of the superconducting fluctuations. As for heavy-fermion superconductors, experimental results are reviewed and several theoretical analyses on the mechanism are provided based on the same viewpoint as explained above.

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“…(15) is correct or not. To clarify this point, we have recently developed an exact numerical algorithm for calculating the DOS of the FGM [8]. For a Gaussian distribution of ∆(x) with zero average and covariance given by Eq.…”

Section: Introductionmentioning

confidence: 99%

“…(5) exactly for a special form of the probability distribution of ∆(x) which is constructed such that its covariance is given by Eq. (8). To begin with, let us perform the following gauge transformation [13],…”

Section: Introductionmentioning

confidence: 99%

Exactly solvable toy model for the pseudogap state

Bartosch

Kopietz

2000

Eur. Phys. J. B

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Abstract. We present an exactly solvable toy model which describes the emergence of a pseudogap in an electronic system due to a fluctuating off-diagonal order parameter. In one dimension our model reduces to the fluctuating gap model (FGM) with a gap ∆(x) that is constrained to be of the form ∆(x) = Ae iQx , where A and Q are random variables. We explicitly calculate the average density of states, the localization length, the average single-particle Green's function, and the real part of the average conductivity. In our model phase fluctuations generate delocalized states at the Fermi energy, which give rise to a finite Drude peak in the conductivity. We also find that the interplay between phase and amplitude fluctuations leads to a weak logarithmic singulatity in the single-particle spectral function at the bare quasi-particle energies. In higher dimensions our model might be relevant to describe the pseudogap state in the underdoped cuprate superconductors.

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Exact numerical calculation of the density of states of the fluctuating gap model

Cited by 31 publications

References 15 publications

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

Nonlinear Schrödinger equation with random Gaussian input: Distribution of inverse scattering data and eigenvalues

Theory of superconductivity in strongly correlated electron systems

Exactly solvable toy model for the pseudogap state

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